To help identify ecosystem and climate influences on American plaice recruitment, distribution, and growth, generalized additive models (GAMs) were used to examine associations between American plaice population dynamics and environmental variables in the Gulf of Maine (GOM) region. This document is meant to serve an a general overview of this analysis. For more details, please refer to Technical Report 16 in Appendix A of the American Plaice Research Track Working Group Report.
Monthly averaged FVCOM data (1978-2019) sourced for bottom water temperature data.
Temperatures were reported as anomalies based on 1981-2010 base period (Same base period as NOAA)
The Northeast Fisheries Science Center (NEFSC) Bottom Trawl Survey.
can be accessed from tables 9a and 9b from: https://apps-nefsc.fisheries.noaa.gov/saw/sasi/uploads/2019_PLA_UNIT_TAB_OA2017_DATA_RESULTS_TABLES.pdf.
Used Spring (Feb-April 1980-2019) and fall (Sept-Oct 1980-2018) data.
R/SSB is a metric of recruitment success (Perretti et al. 2017), denoted as recruit abundance in year t per spawning stock biomass in year t-x , where x =1, (Rt/SSBt-x).
Mean depth and latitude of occurrence (center of gravity), overtime.
The American plaice condition index data were the same used in the 2022 State of the Ecosystem Report, by NOAA Fisheries. https://apps-nefsc.fisheries.noaa.gov/rcb/publications/soe/SOE-NEFMC_2022-Final.pdf. These data represent the ratio of observed weight:predicted weight from the Fall NEFSC survey and span from 1992-2019.
The American plaice weight at age (WAA) anomaly data were calculated from weight at age data used by the American plaice Stock Assessment Research Track working group. These seasonal data are from the NEFSC Survey and span from 1992-2019.
gam((WAA_anomaly)~ s(GSI, k=5)+s(AMO, k=5)+s(NAO, k=5)+s(month6_avg_bt,k=5)+s(yearly_bt, k=5), family=tw(),method = “REML”,data=Fall_distribution.df)
tested without k (default goes to 10). Can’t run full model at default because there are not enough data to support such a high K.
GAMs explore the response based in the mean-centered values.
As such, the y-axis shows values around zero (the mean).
The closer these new (transformed values) are to the zero line, the more it indicates that the smooth curve is basically not explaining the changes in the response.
When the curve is above the zero line, it means the original response value was above the average, and vice versa.
Unlike linear regression, which uses slope, there is no single quantitative coefficient you can make inference from, so you need to rely on interpreting the partial effects of the smooth visually.
Sources:
Tinarwo, Partson. (2019). Re: How to interpret generalized additive model (GAM) summary of statistics in R?. Retrieved from: https://www.researchgate.net/post/How-to-interpret-generalized-additive-model-GAM-summary-of-statistics-in-R/5d0a0acd3d48b7bd46517856/citation/download.
Fonti Kar, D. F. (2022, February). Generalised additive models (GAMS). Environmental Computing. Retrieved June 21, 2022, from https://environmentalcomputing.net/statistics/gams/
In Terms of Recruitment (How to read):
In Terms of Distribution (Depth) (How to read):
In Terms of Distribution (Latitude) (How to read):
In Terms of Growth (How to read):
Original condition index data represent the ratio of observed somatic weight:predicted somatic weight.
If response curve is above the zero mean line, it means the original response was greater than the average = higher condition = fatter fish/length.
If response curve is below the zero mean line, it means the original response was less than than the average = lower condition = thinner fish/length.
Original weight at age data are in units of mean kg at each age/ year.
If response curve is above the zero mean line, it means the original response was greater than the average = greater weight at age.
If response curve is below the zero mean line, it means the original response was less than than the average = lower weight at age.
Pearson correlation coefficient tests revealed high dependence between GSI and temperature variables (bottom temperature & SST), as well as between NAO & AMO.
6 month bottom temperature means are September (year-1) - February (year) for spring survey and April (year-1) - September (year) for fall survey.
Annual bottom temperature means are March (year-1) - February (year) for spring survey and October (year-1) - September (year) for fall survey.
No outliars were removed.
Seasonal R/SSB Age 1
| Model | Significant Covariates | Full Model Deviance Explained | Full Model AIC | Reduced Model Deviance Explained | Reduced Model AIC |
|---|---|---|---|---|---|
| Fall | GSI (1.13%) AMO - 6-month mean (26.0%) |
53.7% | 39.46 | 33.1% | 43.16 |
| Spring | AMO -annual mean (36.6%) | 63.4% | -75.96 | 36.6% | -65.04 |
Model Diagnostics
Fall GAM Relationship Curves
Spring GAM Relationship Curves
Seasonal Mean Depth and Latitude of Catches from NEFSC Bottom Trawl Survey
Spring depth model had no significant variables
SSB and annual bottom temperature anomaly were significant in both latitude models (spring and fall).
Model deviance explained ranged from 55.6-73.9% (See Table Below)
Ultimately picked tweedie distribution for each model, though gaussian and gamma distributions were similar in diagnostics. Picked tweedie for combination of best looking residuals and AIC.
GAM response curves showed consistency between similar significant variables (Figures 2-4)
| Model | Variables Used in Reduced Model (% DE when alone in model) | Full Model Deviance Explained (No Duplicates) | Full Model AIC | Reduced Model Deviance Explained (No duplicates or highly correlated) | Reduced Model AIC |
|---|---|---|---|---|---|
| Fall Depth | NAO - Annual (16.9%) 6-month Bt Anomaly (7.4%) SSB (5.99%) |
55.6% | 264.2 | 53.3% | 262.43 |
| Spring Depth | N/A | N/A | N/A | N/A | N/A |
| Fall Latitude | AMO - 6-Month (3.74%) Annual Bt Anomaly (24.8%) SSB (14.1%) |
70.5% | -77.39 | 60.6% | -75.87 |
| Spring Latitude | NAO - 6-Month (9.39%) Annual Bt Anomaly (33.9%) SSB (14.1%) |
73.9% | -101.22 | 69.5% | -101.40 |
Figure 1: Model fit plots of each season × dependent variable groups. Each Row of plots corresponds to a difference season × dependent variable group where row (1) is fall depth and row (2) is fall latitude, and row (3) is spring latitude.
Figure 2: Fall Mean Depth GAM response curves
Figure 3: Fall Mean Latitude GAM response curves
Figure 4: Spring Mean Latitude GAM response curves
Figure 1: Fall Mean Condition Indices
Figure 2: Fall WAA Anomalies for Plaice Ages 1-5
Figure 3: Fall WAA Anomalies for Plaice Ages 6-11+
Figure 4: Spring WAA Anomalies for Plaice Ages 1-5
Figure 5: Spring WAA Anomalies for Plaice Ages 6-11+
| Model | Significant Covariates | Full Model Deviance Explained | Full Model AIC | Reduced Model Deviance Explained | Reduced Model AIC |
|---|---|---|---|---|---|
| Fall | 6-Month AMO (10.2%) Annual Bottom Temperature Anomaly (12.1%) SSB (25.5%) |
58.3% | -107.28 | 57.5% | -111.255 |
Figure 6: Fall Mean Condition Model Diagnostics
Figure 7: Fall Mean Condition GAM Response Curves
Fall age 8 and Spring age 1 had no significant variables
GSI was significant in younger age classes (2-4 for Fall and ages 2-6 for spring)
AMO was significant in every year class (except age 1 (fall and spring), and in age 8 (fall specifically))
SSB was significant for ages 3-5 in Fall and 5-6 in Spring
Bottom temperature anomalies were significant in more year class extremes (Age 1 & 9 in fall, 10 & 11 in spring)
GAM response curves showed consistency between similar significant variables (Figures 11-14)
Figure 8: Visualizing Significant Variables by Year Class
Table 1: Fall Model Results
Table 2: Spring Model Results
Figure 9: Model diagnostic fit plots for fall
Figure 10: Model diagnostic fit plots for spring
Figure 11: Fall Ages 1-5 WAA Anomlay GAM response curves
Figure 12: Fall Ages 5-11+ WAA Anomlay GAM response curves
Figure 13: Spring Ages 2-4 WAA Anomlay GAM response curves
Figure 14: Fall Ages 5-11+ WAA Anomlay GAM response curves
GAM response curve plots are difficult to read, but are meant to show consistency of trends/curve shapes
Gaussian GAMs were used and covariates were selected after applying a backwards fitting technique based on covariate significance (p<0.05) and AIC.